Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
int main() {
  using D = double;
  int N;
  cin >> N;
  vector<D> a(N);
  for(auto& i: a) cin >> i;
  sort(begin(a), end(a));
  D ans = 0;
  for(auto j = 1; j < N; ++j) for(auto i = 0; i < j; ++i) {
    auto y = N - 1;
    for(auto k: {j, i}) if(y == k) --y;
    auto x = y - 1;
    for(auto k: {j, i}) if(x == k) --x;
    ans = max(ans, (a[y] + a[x]) / (a[j] - a[i]));
  }
  cout << setprecision(8) << fixed << ans << endl;
}